Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
ENG
Логин:
Пароль:

Structural adaptive inference

Описание направления:

Structural adaptive inference provide basis for most of data analysis algorithms developed at PreMoLab. This approach enables efficient analysis of complex statistical models.

Within the recent years a series of innovative approaches and algorithms such as adaptive weights smoothing (AWS), propagation separation (PS), local model selection (LMS), stagewise aggregation (SA) and local change point detection (LCP) has been developed. All these procedures are based on a new local parametric approach and have been justified in a series of theoretical publications.

In this context important problems and questions in the field of modern parametric and nonparametric methods including problems of automatic selection of smoothing parameters in case of qualitative structural assumptions statistics have been solved. Structural adaptive methods have been also developed and adapted for several classes of statistical models and methods such as structure extraction, pattern recognition and universal coding.

Публикации:

Evidence optimization for consequently generated method

Преподаватели: Крымова Екатерина , Strijov, V, Weber, GW, 16 ноября 2014

Local Quantile Regression (with rejoinder)

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile curve is not a priori fixed. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimator of the conditional quantile curve requires to balance between local curvature and stochastic variability. In this paper, we suggest a local model selection technique that provides an adaptive estimator of the conditional quantile regression curve at each design point. Theoretical results claim that the proposed adaptive procedure performs as good as an oracle which would minimize the local estimation risk for the problem at hand. We illustrate the performance of the procedure by an extensive simulation study and consider a couple of applications: to tail dependence analysis for the Hong Kong stock market and to analysis of the distributions of the risk factors of temperature dynamics.

Преподаватели: Спокойный Владимир Григорьевич, Wang, W, H?rdle, W, 16 ноября 2014

Manifold Learning: generalizing ability and tangential proximity

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional Data Manifold (DM) embedded in a high-dimensional observation space from a given set of data points sampled from the manifold. We derive asymptotic expansion and local lower and upper bounds for the maximum reconstruction error in a small neighborhood of an arbitrary point. The expansion and bounds are defined in terms of the distance between tangent spaces to the original Data manifold and the Reconstructed Manifold (RM) at the selected point and its reconstructed value, respectively. We propose an amplification of the ML, called Tangent Bundle ML, in which proximity is required not only between the DM and RM but also between their tangent spaces. We present a new geometrically motivated Grassman&Stiefel Eigenmaps algorithm that solves this problem and gives a new solution for the ML also.

Преподаватели: Бернштейн Александр Владимирович, Kuleshov, AP, 16 ноября 2014

Modeling Nonstationary and Leptokurtic Financial Time Series

Financial time series is often assumed to be stationary and has a normal distribution in the literature. Both assumptions are however unrealistic. This paper proposes a new methodology with a focus on volatility estimation that is able to account for nonstationarity and heavy tails simultaneously. In particular, a local exponential smoothing (LES) approach is developed, in which weak estimates with different memory parameter are aggregated in a locally adaptive way. The procedure is fully automatic, the parameter are tuned by a new propagation approach. The extensive and practically oriented numerical results confirm the desired properties of the constructed estimate: it performs stable in a nearly time homogeneous situation and is sensitive to structural shifts. Our main theoretical ``oracle'' result claims that the aggregated estimate performs as good as the best estimate in the considered family. The results are stated under realistic and unrestrictive assumptions on the model.

Преподаватели: Спокойный Владимир Григорьевич, Chen, Y, 16 ноября 2014

Sparse Non Gaussian Component Analysis by Semidefinite Programming

Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinite programming which improves the method sensitivity to a broad variety of deviations from normality. We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.

Преподаватели: Спокойный Владимир Григорьевич, Немировский Аркадий Семенович, Diederichs, E, Juditsky, 16 ноября 2014

Прошедшие мероприятия:

16.02.2015
Independent University of Moscow

Model Selection

Mini-Course on Model SelectionBrief table of content1. Gaussian model selection by unbiased risk estimation (SURE)2. "Largest accepted" method for projection estimation3. Model selection for linear smoothers4. Sieve model selection and uniform Wilks expansion 5. Local parametric estimation and bandwidth selection 6. Bootstrap parameter tuning

15.05.2014

16.05.2014

Advances in Optimization and Statistics

Institute of Information Transmission Problems of RAS (Kharkevich Institute)

21.02.2014

PreMoLab 2014 - I

Institute of Information Transmission Problems of RAS (Kharkevich Institute). Конференция пройдет в Институте проблем передачи информации РАН (ИППИ РАН), к.615

26.12.2013

New trends in Predictive Modeling

Institute of Information Transmission Problems of RAS (Kharkevich Institute). All talks take place at Institute for Information Transmission Problems (B. Karetny, 19).

22.12.2013

Parametric statistics: modern view. Premoday, December 2012

Члены лаборатории:
Spokoiny Vladimir
Должность: Руководитель
Golubev Yuri
Должность: Ведущий научный сотрудник
Nesterov Yurii
Должность: Ведущий научный сотрудник
Belyaev Mikhail
Должность: Младший научный сотрудник
Bernshtein Alexander
Должность: Ведущий научный сотрудник
Krymova Ekaterina
Должность: Младший научный сотрудник
Panov Maxim
Должность: Младший научный сотрудник
Prihodko Pavel
Должность: Младший научный сотрудник
Burnaev Evgeny
Должность: Ведущий научный сотрудник